Based on Lemma 1 in [1]} and Lemma 1 in [2]}, \(p(\mathbf {z}|\mathcal {C})\)  is equivalent to rejection sampling with proposal distribution \(p_{\mathbf {z}}(\mathbf {z})\)  and acceptance probability
\(r(\mathbf {z}) = \frac{e^{-E_{\mathcal {C}}(G(\mathbf {z}))}}{M_{\mathcal {C}}\cdot Z}, \quad \text{where } \forall \mathbf {z}, M_{\mathcal {C}} > \frac{e^{-E_{\mathcal {C}}(G(\mathbf {z}))}}{Z}.\) 
